Circuits for producing non-linear voltages



P 1958 H. G. BOYLE 2,854,622

CIRCUITS FOR PRODUCING NON-LINEAR VOLTAGES Filed May 29, 1957 INVENTOR.HOMER s. BOYLE. a! M. pe 1W7? G 2 ATTOR EYS.

United States Patent CIRCUITS FOR PRODUCING NON-LINEAR VOLTAGES Homer G.Boyle, Dayton, Ohio, assignor to Avco Manufacturing Corporation,Cincinnati, Ohio, a corporation of Delaware Application May 29, 1957,Serial No. 662,397

17 Claims. (Cl. 323-74) This invention relates to a variable impedancenetwork and, more particularly, to a voltage divider network employinglinear resistance elements for deriving non-linear functions.

In many applications it is necessary to convert the linear rotation of ashaft into a non-linear, electrical function. When the non-linearfunction is complex, it has been the general practice to wind anelectrical impedance element on a form shaped in such a manner that therequired function is produced; or the rotation of the shaft may beconverted by mechanical means into a non-linear motion by means of cams,etc. In many cases a special card is required. All of these methodsentail individual winding, calibration and tailoring, which areextremely time-consuming and expensive. On the other hand, there areavailable on the market linear and first-order variable impedances whichcan be duplicated in production quantities with very high accuracy, andit would be very advantageous to use impedances of this type to producethe required results.

It is, therefore, an object of the invention to provide a non-linear,variable impedance device constructed entirely of linear elements.

Another object of this invention is the provision of a short-circuited,linear potentiometer for producing nonlinear impedances.

Still another object of this invention is the provision of at least twoshort-circuited, linear potentiometers, each having a grounded tap andconnected in parallel for producing non-linear, complex impedances.

Another object of this invention is to provide an impedance networkcomprising single or plural potentiometers composed of linear elementsdriven from a single shaft and capable of producing complex functions.

For a more complete understanding of the nature and objects of thisinvention, reference should be had to the following detailed descriptionand to the accompanying drawing in which the single figure represents apreferred form of my invention.

Briefly stated, the invention comprises a first potentiometer connectedin series with at least one short-circuited potentiometer, the movabletap of which is connected to ground. With this arrangement, and byproper selection of the values of the resistances in the network, eachof which is linear, almost any complex curve can be duplicated.

Referring to the drawing, a first linear potentiometer 1, havingvariable resistance values of R and R above and below the movable tap 2,respectively, is connected at one end to a source of reference potential3 and at the other end to a short-circuited dual potentiometercomprising first and second parallel branches, bothvshortcircuited bythe line 4. Depending on the complexity of the curve to be duplicated,any number of branches may be used. For example, if the curve isbasically a parabola, then only one branch is required. If the curve ismore complex, two or more branches may be used. The

Patented Sept. 30, 1958 two branches shown are merely a convenientnumber for illustrating the invention.

The first branch comprises a potentiometer 5 having variable resistancevalues R and R above and below the tap 6, respectively, and aseries-connected resistor 7 having a fixed resistance value R Similarly,the second branch comprises a potentiometer 8 having variable resistancevalues R and R on each side of the movable potentiometer tap 9, asindicated, and a series-connected resistor 10 having a fixed resistancevalue R While I have shown only one fixed resistor in each branch, it isto be understood that the resistors 7 and 10 may be variable. It is alsoto be understood that the resistors 7 and 10 may be positioned on theopposite side of the resistors 5 and 8 to reverse the slope of theresultant curves and, also that additional fixed or variable resistorsmay be inserted in each branch.

The taps 2, 6 and 9 are mechanically coupled to a shaft 11 from whichall are simultaneously driven. The shaft 11 may be driven by a referenceelement in a servo system, or it may be the input to a computer or othertype of system,not shown. The taps 6 and 9 are both electricallyconnected to ground or other point of reference potential by means of alead 12. The output is taken from the terminals 13 connected between thetap 2 and ground.

If we consider the dual potentiometer with the second branchdisconnected, and with the resistor 7 having a resistance value R equalto zero, movement of the tap 6 along the resistor 5 will produce aresultant of two reciprocal linear curves, a solution which is asymmetrical parabola. By proper selection of elements 5 and 7 of thefirst branch, the resultant voltage at the tap 2 may have similar orvastly dissimilar slopes to the sides of the parabola. If an output isderived with identical elements in the first branch, that is, R +R =Rthe resultant will be a lambda function, and this may be used, forexample, as an error voltage for the servo control of mechanical driventuning cavities or lines.

By a proper selection of values for the potentiometer 1 and the elementsin each branch, logarithmic or asymptotic functions may be obtained inboth branches and, with all the branches connected and the potentiometertaps 2, 6 and 9 arranged for movement in unison or in opposition, higherorder effects may be obtained.

Where n number of branches are employed, the impedance R of the networkbetween the terminals 13 will be represented as follows:

where Cu'i' RDn+ RE and, therefore:

not contain sharp breaks or steps, a practical solution of a completepotentiometer card problem can be resolved by plotting about ten pointswith approximately thirtydegree distribution. These points are derivedquickly by simple calculations, using standard, commercial, closetolerance, ganged potentiometers connected as shown, and the desiredfunctions can be produced as accurately as with the expensive,custom-wound and calibrated card. The solution of almost any curve canbe accomplished quickly and accurately by manual or machinecalculations.

It may now be seen that from a very simple arrangement of entirelylinear elements, I am able to produce impedances which vary inaccordance with very complex and high-order functions. It is clear thatcertain modifications and variations will be apparent to those skilledin the art, and it is my intention, therefore, that my invention belimited only by the prior art and the annexed claims.

What I claim is:

l. A variable impedance network comprising: at least first and secondparallel connected impedance elements, each provided with a movable tapand the ends of each element being connected to a point of referencepotenial; and means for simultaneously varying the position of said tapson said impedances at a linear rate, whereby the overall impedance ofsaid network between said point and said taps will vary at a non-linearrate.

2. The invention as defined in claim 1, wherein said impedance elementsare linear elements.

3. The invention as defined in claim 2, wherein said linear elements areresistors.

4. A variable impedance device comprising: at least first and secondparallel connected impedance elements, each having a first movable tapand the ends of each element being connected to a point of referencepotential; a third impedance element connected to said point; said thirdimpedance element having a second movable tap; and means forsimultaneously varying the position of all said movable taps on saidelements at a linear rate, whereby the value of impedance between saidfirst and second taps varies in accordance with a predeterminednonlinear function.

5. The invention as defined in claim 4, wherein each of said impedanceelements is a linear resistance element.

6. A variable voltage device comprising a source of reference potentialconnected across a variable impedance network, said variable impedancenetwork comprising: a first impedance having a movable tap and a secondimpedance having a movable tap, one end of said first impedance beingconnected to one side of said source, the other end of said firstimpedance being connected to both ends of said second impedance, the tapof said second impedance being connected to the other side of saidsource; and means for moving said taps on said impedances at a linearrate, whereby a non-linear output between said taps is produced.

7. The invention as defined in claim 6, wherein said impedances arelinear.

8. A variable voltage device comprising: a first impedance branch havingfirst and second series-connected resistors, said first resistor havinga first movable tap; a second branch connected in parallel with saidfirst branch and having third and fourth series-connected resistors,said third resistor having a second movable tap, both ends of saidbranches being connected to a fifth resistor having a third movable tap;a source of potential connected across said fifth resistor and thejunction of said first and second taps; and means for simultaneouslymoving said taps at a linear rate, whereby the voltage between thejunction of said first and second taps and said third tap will vary at anon-linear rate.

9. A variable impedance device comprising: 12 parallel connectedbranches, where n equals any whole number, both ends of each of saidbranches being connected to a point of reference potential; each of saidbranches comprising a resistor provided with a movable tap; means forelectrically interconnecting each of said taps; and means forsimultaneously varying the position of said taps on said resistors at alinear rate.

10. The invention as defined in claim 9 wherein a voltage source isconnected between said point of reference potential and said taps, andwherein n equals 1.

11. A system for converting the linear rotation of a shaft into anon-linear voltage comprising: a first resistor having a first movabletap coupled to said shaft; a variable impcdance having at least a firstbranch, each branch comprising a second resistor having a second movabletap coupled to said shaft; means connecting both ends of said secondresistor to one end of said first resistor; a source of potentialconnected between the other end of said first resistor and said secondmovable tap; and means for deriving a resultant voltage output frombetween said second movable tap and said first movable tap.

12. The invention as defined in claim 1], wherein each of said resistorsis a linear element.

13. A variable impedance device comprising: 11 parallel connectedbranches, where n equals any whole number, both ends of each of saidbranches being connected to a point of reference potential; each of saidbranches comprising first and second series-connected resistors; each ofsaid first resistors being provided with a movable tap; all of saidmovable taps being electrically interconnected; and means forsimultaneously varying the position of each of said taps at a linearrate.

14. The invention as defined in claim 13, wherein said impedance isdesigned in accordance with the equation:

where R equals the total impedance measured between said point ofreference potential and said movable taps; and R R and R are equal,respectively, to the impedance of each branch between said point ofreference potential and said tap measured independently of all otherbranches.

15. The invention as defined in claim 13, where each of said resistorsis a linear element.

16. The invention as defined in claim 12, and another resistorseries-connected with said variable impedance device, said resistorhaving a movable output tap.

17. The invention as defined in claim 16, wherein said other resistorand said variable impedance device are designed in accordance with thefollowing equation:

References Cited in the file of this patent UNITED STATES PATENTSNielsen et al. Dec. 9, 1952 Brancato et al. Mar. 17, 1953

